On generalized invariants of injective nonsingular module algebras (Q1970964)

The authors study the ``generalized invariants'' \(A_V\) of an \(H\)-module algebra \(A\); where \(H\) is a Hopf algebra over a field \(k\) and \(V\) is a suitable subspace of its restricted dual \(H^o\). In particular, the algebra of invariants \(A^H\) is \(A_V\) for \(V=k\varepsilon\). It is shown that, if \(A\) is injective and non-singular as \(A^H\)-module, then so is \(A_V\) for any finite dimensional \(V\). Consequences, variations and examples of this theme are explored.